This book is a collection of papers from the 9th International ISAAC Congress held in 2013 in Kraków, Poland. The papers are devoted to recent results in mathematics, focused on analysis and a wide range of its applications. These include up-to-date findings of the following topics:- Differential Equations: Complex and Functional Analytic Methods- Nonlinear PDE- Qualitative Properties of Evolution Models- Differential and Difference Equations- Toeplitz Operators- Wavelet Theory- Topological and Geometrical Methods of Analysis- Queueing Theory and Performance Evaluation of Computer Networks- Clifford and Quaternion Analysis- Fixed Point Theory- M-Frame Constructions- Spaces of Differentiable Functions of Several Real VariablesGeneralized Functions- Analytic Methods in Complex Geometry- Topological and Geometrical Methods of Analysis- Integral Transforms and Reproducing Kernels- Didactical Approaches to Mathematical ThinkingTheir wide applications in biomathematics, mechanics, queueing models, scattering, geomechanics etc. are presented in a concise, but comprehensible way, such that further ramifications and future directions can be immediately seen.